To be able to attach ultrasonic sensors to the vehicle invisibly from the outside and protected from environmental influences, in particular when using surroundings detection systems of motor vehicles, it is conventional to provide ultrasonic transducers which are situated hidden, i.e., invisibly from the outside, on internal surfaces of lining or body elements, for example on an internal surface of a bumper.
An ultrasonic sensor is described in U.S. Published Application No. 2010/0020646 A1, for example, which is designed in the form of a thickness oscillator and suitable for a hidden installation. Proceeding from a piezoceramic including electrodes, at least one front element is provided, which has such a shape that a desired directional characteristic is created. The length of the transmission path corresponds to λ/4 at the resonance frequency fR, so that an amplification of the oscillation, proceeding from the piezoceramic, is achieved on the radiating surface. It is furthermore shown that a λ/2 oscillator is preferably used for some applications, which is more robust in particular with respect to temperature stability, susceptibility to soiling, and deposits. The λ/2 oscillator described in U.S. Published Application No. 2010/0020646 A1 includes a front element and a rear element, the respective length of the front and rear elements, plus half of the thickness of the piezoceramic disk, corresponding to one quarter of the wavelength A of the sound in the particular material. U.S. Published Application No. 2010/0208553 A1 describes a similar configuration.
In such configurations, which provide a sound transducer which may be mounted invisibly behind a lining element, for example the bumper of a vehicle, an area of the lining element is induced to oscillate by excitation of the sound transducer. This area, in turn, emits sound and thus acts as a diaphragm. According to the same active principle, incident sound may induce the diaphragm to oscillate and prompt the sound transducer to generate a corresponding electrical signal. Such a sensor system, as described in U.S. Published Application No. 2010/0208553 A1 for example, is schematically shown in FIG. 1. Such a configuration has the disadvantage that the free end of rear element 30 oscillates freely and may thereby emit inadvertent sound. In addition, mechanical impacts may result in a high load on the adhesive bonds, in particular due to tensile stresses, when the sound transducer is mounted on the rear element, in particular with a horizontal installation. U.S. Published Application No. 2010/0208553 A1 describes that a mounting in the area above the piezoceramic is possible to avoid these problems. It is not advantageous to mount the rear element since this would impair the λ/4 oscillation of the rear element.
In the specification of the wavelength, it should be noted that the wavelength A of an oscillation generally results as a quotient from the propagation velocity cS (sound velocity) and the frequency f of the oscillation:λ=cs/f. 
Since the frequency f is predefined in such sensor systems (by the excitation of the piezoelectric element or by the frequency of the incident sound waves) and the propagation velocity cs is generally material-dependent, a different wavelength λv may possibly result for the front area of the thickness oscillator (front element, diaphragm) than for the rear area (rear element), where the wavelength λr arises.